A train travels from station P to station Q and immediately returns to station P along the same track.
• On the outward trip it moves at a constant speed of 60km/h.
• On the return trip it moves at a constant speed of 20m/s.
The distances between the two stations are equal in both directions.
(i) Derive a general expression for the average speed vavg of a round trip in which equal distances are covered at two different constant speeds v1 and v2.
(ii) Using your expression, calculate the train’s average speed for the complete journey. Express the answer in km/h, correct to one decimal place.
(iii) What is the train’s average velocity for the entire to-and-fro motion? State a reason for your answer.